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Linear Identification of Linear Rational-Expectations Models by Exogenous Variables Reconciles Lucas and Sims

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  • Peter A. Zadrozny

Abstract

Linear rational-expectations models (LREMs) are usually “forwardly” estimated. Structural coefficients are restricted in terms of deep parameters. For given deep parameters, structural equations are solved for rational-expectations solution (RES) eqs. that determine endogenous variables. For given VAR eqs. that determine exogenous variables (XVAR), RES eqs. reduce to reduced-form VAR eqs. with exogenous variables (ERF). Combined XVAR and ERF eqs. comprise reduced-form (RF) overall VAR (OVAR) eqs. of all variables. The specified, solved, and combined eqs. define a mapping from deep parameters to OVAR coefficients used to forwardly est. a LREM in terms of deep parameters. Forwardly-est. deep parameters determine forwardly-est. RES eqs. that Lucas (1976) advocated for making policy predictions. Sims (1980) called identifying restrictions on deep parameters of forwardly-est. LREMs “incredible”, because he considered in-sample fits of forwardly-est. OVAR eqs. inadequate and out-of-sample policy predictions of forwardly-est. RES eqs. inaccurate. Sims (1980, 1986) instead advocated directly estimating OVAR eqs. restricted by statistical restrictions and directly using directly-est. OVAR eqs. To make policy predictions. However, if assumed or predicted out-of-sample exogenous policy variables differ significantly from predictions of their in-sample est. XVAR eqs., then, out-of-sample policy predictions of endogenous variables made with OVAR eqs. won’t satisfy Lucas’s critique. If directly-est. OVAR eqs. are RF eqs. of underlying RES eqs., then, identification 2 derived in the paper linearly “inversely” est. the underlying RES eqs. from the directly-est. OVAR eqs. and the inversely- est. RES eqs. can be used to make policy predictions that satisfy Lucas's critique. If Sims considered directly-est. OVAR eqs. to fit in-sample data adequately (credibly) and their inversely-est. RES eqs. To make accurate (credible) out-of-sample policy predictions, then, he should consider the inversely-est. RES eqs. and further underlying LREM- structural eqs. to be credible. Thus, inversely-est. RES eqs. by identification 2 would reconcile Lucas’s advocacy for making policy predictions with RES eqs. and Sims’s advocacy for directly estimating OVAR eqs.

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  • Peter A. Zadrozny, 2022. "Linear Identification of Linear Rational-Expectations Models by Exogenous Variables Reconciles Lucas and Sims," CESifo Working Paper Series 10078, CESifo.
    • Handle: RePEc:ces:ceswps:_10078
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    1. Al-Sadoon, Majid M., 2018. "The Linear Systems Approach To Linear Rational Expectations Models," Econometric Theory, Cambridge University Press, vol. 34(3), pages 628-658, June.
    2. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    3. Taylor, John B, 1979. "Staggered Wage Setting in a Macro Model," American Economic Review, American Economic Association, vol. 69(2), pages 108-113, May.
    4. Zhongjun Qu & Denis Tkachenko, 2017. "Global Identification in DSGE Models Allowing for Indeterminacy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(3), pages 1306-1345.
    5. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
    6. Iskrev, Nikolay, 2010. "Local identification in DSGE models," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 189-202, March.
    7. Taylor, John B, 1980. "Aggregate Dynamics and Staggered Contracts," Journal of Political Economy, University of Chicago Press, vol. 88(1), pages 1-23, February.
    8. Zhongjun Qu & Denis Tkachenko, 2012. "Identification and frequency domain quasi‐maximum likelihood estimation of linearized dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 3(1), pages 95-132, March.
    9. Majid M. Al-Sadoon & Piotr Zwiernik, 2019. "The Identification Problem for Linear Rational Expectations Models," Working Papers 1114, Barcelona School of Economics.
    10. Zadrozny, Peter A., 2016. "Extended Yule–Walker identification of VARMA models with single- or mixed-frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 438-446.
    11. Farmer, Roger E.A. & Khramov, Vadim & Nicolò, Giovanni, 2015. "Solving and estimating indeterminate DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 54(C), pages 17-36.
    12. Andrzej Kocięcki & Marcin Kolasa, 2018. "Global identification of linearized DSGE models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1243-1263, November.
    13. Ivana Komunjer & Serena Ng, 2011. "Dynamic Identification of Dynamic Stochastic General Equilibrium Models," Econometrica, Econometric Society, vol. 79(6), pages 1995-2032, November.
    14. Hansen, Lars Peter & Sargent, Thomas J, 1983. "The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities," Econometrica, Econometric Society, vol. 51(2), pages 377-387, March.
    15. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
    16. Onatski, Alexei, 2006. "Winding number criterion for existence and uniqueness of equilibrium in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 323-345, February.
    17. Lubik, Thomas A. & Schorfheide, Frank, 2003. "Computing sunspot equilibria in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 273-285, November.
    18. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    19. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    20. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
    21. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    22. A Tank & E B Fox & A Shojaie, 2019. "Identifiability and estimation of structural vector autoregressive models for subsampled and mixed-frequency time series," Biometrika, Biometrika Trust, vol. 106(2), pages 433-452.
    23. Taylor, John B, 1977. "Conditions for Unique Solutions in Stochastic Macroeconomic Models with Rational Expectations," Econometrica, Econometric Society, vol. 45(6), pages 1377-1385, September.
    24. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
    25. Funovits, Bernd, 2017. "The full set of solutions of linear rational expectations models," Economics Letters, Elsevier, vol. 161(C), pages 47-51.
    26. Zadrozny, Peter A., 1998. "An eigenvalue method of undetermined coefficients for solving linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1353-1373, August.
    27. Sargent, Thomas J., 1993. "Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198288695.
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    Cited by:

    1. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).

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    More about this item

    Keywords

    cross-equation restrictions of rational expectations; factorization of matrix polynomials; reconciliation of Lucas’s advocacy of rational-expectations modelling and policy predictions and Sims’s advocacy of VAR modelling;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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